I havd done exactly this on No4 20 bore. I did use some walnut which i had available well seasoned oak should be fine, and it holds screw well. If the wood gets wet enough for differential expansion i think a split stock will be least of your concerns. Provided the wood is well seasoned, and the gun is stored properly you shouldn't have a problem. If you use it as a canoe paddle then perhaps. But i have a 71 yeat old boat built of mahogany on oak frames and its not suffering.